Helpppppppppppp meeee
1 answer:
Answer:
25 + 30z³ + 29z² + 12z + 4
Step-by-step explanation:
(5z² + 3z + 2)²
= (5z² + 3z + 2)(5z² + 3z + 2)
Each term in the second factor is multiplied by each term in the first factor, that is
5z²(5z² + 3z + 2) + 3z(5z² + 3z + 2) + 2(5z² + 3z + 2) ← distribute parenthesis
= 25 + 15z³ + 10z² + 15z³ + 9z² + 6z + 10z² + 6z + 4 ← collect like terms
= 25 + 30z³ + 29z² + 12z + 4
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You can find the remainder right away by simply plugging in 
. The polynomial remainder theorem guarantees that the value of 
is the remainder upon dividing 
by 
, but I digress...
Synthetic division yields
3 | 2 -11 18 -15
. | 6 -15 9
- - - - - - - - - - - - - - - - -
. | 2 -5 3 -6
which translates to
(and note that
, as expected)
Synthetic division yields
3 | 2 -11 18 -15
. | 6 -15 9
- - - - - - - - - - - - - - - - -
. | 2 -5 3 -6
which translates to
(and note that
Answer:
250 miles
Step-by-step explanation:
The given distance between the house and the beach is 125 miles.
Let miles be the distance between the house and the lunch stop.
So, at the time of the lunch stop, he already traveled miles, the remaining distance is the distance between the lunch stop and the beach.
Let miles be the remaining distance, so
Give that the ratio of the distance he has traveled, , to the distance he still has to travel,
, is
,i.e
Hence, the distance traveled by Herman when he stops for lunch is 250 miles.